The satirical show is inspired by US reality series The Real Housewives of Orange County

The “show” — based on American series The Real Housewives of Orange County — is part of a new six-parter written by Bafta-winning writers Heydon Prowse and Jolyon Rubinstein, the duo behind The Revolution Will Be Televised.

In the first episode, which also touches on other topics including drones, the NHS budget deficit and abortion law, another actress, in the traditional Muslim headgear, is seen scrubbing the floor of a run-down house.

As she struggles to move around the kitchen, she says: “Ali bought me a new chain which is 8ft long. So I can get outside, which is great.”

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Co-writer Heydon said the BBC had passed the sketch without demanding any cuts to controversial gags.

He said: “It’s important not to pull your punches in satire. You have to be fearless or it undermines your credibility. You can’t go after David Cameron for five years like we did and not go after Islamic State.”

His co-writer, who also stars in the programme, said the target of the jokes is “online grooming”, not ISIS.

Jolyon said: “It’s about people who are vulnerable to these kind of approaches. We’ve had the ‘White Widow’ [British-born terror suspect Samantha Lewthwaite], so this is actually happening to women here.”